Doping Windows

Overview

Doping windows are used to specify an implant/diffusion doping profile through a window. The vertical profile maybe a Gaussian, a complementary Error function or a user specified profile. Doping windows can also be projected in the upward or downward directions or even in both directions simultaneously. The doping profile of a device is built-up using region doping and horizontal doping windows, which are summed to give a total doping concentration.

Usage Instructions

To define a doping window:

1. From the Menu, select Define -> Window -> Doping.

2. Use your cursor and mouse buttons to define a rectangular doping window.

3. Once the window's shape has been defined the doping window's properties dialog box will appear. Use this dialog to set the window's properties.

Parameters

General

Name	Description	Unit
Name	A unique identifier for the window.	-
Colour	Used to define visual colour of the region (Not used in the solver).	-
Edge Symmetry	Used to select the shape of the diffusion. Options: [Normal, Left Symmetric, Right Symmetric or Double Symmetric]	-
Direction	Used to select the direction of the implant. Options: [Upwards, Downwards, Both]	-
Doping	Used to specify the type of doping implant. Options: [Donor, Acceptor]	-

Available materials include Si, SiC, Oxide, Air (more coming soon). The properties of these materials can be fully customised by the user during setup of the device model. There are two general types of semiconductor can be defined, namely:

• Single Composition (e.g. Si, GaAs, SiC)
• Variable Composition (e.g. AlGaN, AlGaAs).

Doping

Name	Description	Unit
Acceptor	Used to define the acceptor doping concentration in the region.	Atoms/cm³
Donor	Used to define the donor doping concentration in the region.	Atoms/cm³

Composition (Coming soon)

After a region has been defined, the user can specify a constant compositional profile over the region. The mole fraction X for a ternary compound and both X and Y mole fractions for quaternary materials can be specified. This command sets a constant values in a specified region.

Name	Description	Unit
Mole Fraction X	Used to define the acceptor doping concentration in the region.	Atoms/cm³
Mole Fraction Y	Used to define the donor doping concentration in the region.	Atoms/cm³

Calculation of Vertical Diffusions

Vertical Gaussian Scaling Factor

$$y_{fact} = N_0 \exp \left( -\frac{y - y_{offset}}{\sigma_v} \right)$$

note

Check this equation

• $N_0$ is the Peak doping concentration, given as the first vertical parameter.
• $y$ is the distance in y direction below/above window.
• $\sigma_v$ is the vertical straddle, given as 2nd vertical parameter.
• $y_{offset}$ is the offset of vertical peak below window, given as 3rd vertical parameter.

Vertical Erfc Scaling Factor

$$y_{\text{fact}} = N_0 \operatorname{erfc} \left( \frac{y}{\sigma_v} \right)$$

• $N_0$ is the Peak doping concentration, given as the first vertical parameter.
• $y$ is the distance in y direction below/above window.
• $\sigma_v$ is the vertical straddle, given as 2nd vertical parameter.
• $y_{offset}$ is the offset of vertical peak below window, given as 3rd vertical parameter.

Vertical User Defined Scaling Factor

$$y_{\text{fact}} = y_{\text{user}} \left( {y} \right)$$

• $N_0$ is the Peak doping concentration, given as the first vertical parameter.
• $y$ is the distance in y direction below/above window.
• $y_{\text{user}} \left( {y} \right)$ is the user profile.
• $\sigma_v$ is the vertical straddle, given as 2nd vertical parameter.
• $y_{offset}$ is the offset of vertical peak below window, given as 3rd vertical parameter.

Calculation of Lateral Diffusions

The lateral extent of the profile is controlled by the point types, and the lateral choice.

Lateral Rotation Scaling Factor

The lateral rotation scaling factor defines a series of elliptical contours for the lateral profile. Its value ranges from 0 to 1, where 1 represents a circular shape. Typically, values between 0.5 and 0.8 are used.

For $x$ outside window:

$$x_{\text{fact}} = \sqrt{\left(\frac{x - x_w}{r}\right)^2 + y^2}$$

Otherwise:

$$x_{\text{fact}} = 1$$

• $x$ is the current x coordinate.
• $x_w$ is either window edge.
• $y$ is the distance in y direction below/above window.
• $r$ is the Radial reduction factor, given as 1st lateral parameter.

Lateral Erfc Scaling Factor

If both points are window points:

$$x_{\text{fact}} = \operatorname{erfc}{\left(\frac{x - x_y}{\sigma_l}\right) - \operatorname{erfc}\left(\frac{x - x_l}{\sigma_l}\right) }$$

If only a left point is a window point:

$$x_{\text{fact}} = -\operatorname{erfc}\left(\frac{x - x_l}{\sigma_l}\right)^2$$

If only a right point is a window point:

$$x_{\text{fact}} = \operatorname{erfc}\left(\frac{x - x_y}{\sigma_l}\right)^2$$

If neither point is a window point:

$$x_{\text{fact}} = 1$$

• $y$ is the distance in y direction below/above window.
• $\sigma_l$ is the lateral straddle, given as 1st lateral parameter.

Total Doping

The total doping at point is defined as:

$$N(x, y) = x_{\text{fact}} \cdot y_{\text{fact}}$$